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How to calculate underwater explosions?

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Liger686

Liger686

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How would I go about calculating an explosion that went off underwater?
 
I don't think anyone has developed such a equation or theory of underwater explosion, in my previous research I've only found airburst and surface explosions.
 
The same as a surface one, except much worse because the air isn't going to absorb a portion of the pressure generated by the explosion. It is going to increase it. You'll be subject to the entire yield of the blast, unimpeded by anything, due to the water's incompressibility.
 
Kal did a calc of a nuke going off under water a little while back, though I do recall him saying it was a low end due to factors he couldn't properly calculate.
 
Kaltias used KE since the explosion created a vacuum; in real conditions that will never happen.
 
It was either Lina or TTGL who did a calc for Atlantis involving the KE of The Ulysses moving underwater. I'm not sure if it's applicable, though.
 
Probably calc the volume of the area taken up by the explosion, and use the radius as the distance for KE.
 
If what Kep and antonio said is true, then expect downgrades for calcs in similar scenerios.
 
Azathoth the Abyssal Idiot said:
Kal did a calc of a nuke going off under water a little while back, though I do recall him saying it was a low end due to factors he couldn't properly calculate.
Click to expand...
It's a lowball because it keeps expanding for a bit while off screen (which can't be calced due to cinematic timing), but the method itself isn't lowballed
 
@SomebodyData

I'm pretty sure Kep is saying that the explosion would be more powerful underwater than on the surface.
 
Hmmn makes sense. Wikipedia says this: Mass and incompressibility (all explosions) ― water has a much higher density than air, which makes water harder to move (higher inertia). It is also relatively hard to compress (increase density) when under pressure in a low range, say up to 100 atmospheres. These two together make water an excellent conductor of shock waves from an explosion.

Problem: How exactly do we calc this?
 
So I found this article on Wikipedia.

https://en.wikipedia.org/wiki/Underwater_explosion#Shallow_underwater_explosio

For shallow underwater explosions, a 20 kiloton warhead was detonated in a lagoon which was approximately 200 ft (61 m) deep. You can read the effects on Wikipedia.

https://en.wikipedia.org/wiki/Underwater_explosion#Deep_underwater_explosio

For deep water explosions, a 9 kt Mk-7 was detonated at a depth of 500 ft (150 m) in deep water. Again you can see the effects on the Wikipedia article I linked.

Would this be useful, eg to use as a base or something?
 
Quoting from the 9 kiloton explosion:

"he heights of surface waves generated by deep underwater explosions are greater because more energy is delivered to the water. During the Cold War, underwater explosions were thought to operate under the same principles as tsunamis, potentially increasing dramatically in height as they move over shallow water, and flooding the land beyond the shoreline.[6] Later research and analysis suggested that water waves generated by explosions were different from those generated by tsunamis and landslides. Méhauté et al. conclude in their 1996 overview Water Waves Generated by Underwater Explosion that the surface waves from even a very large offshore undersea explosion would expend most of their energy on the continental shelf, resulting in coastal flooding no worse than that from a bad storm."

I believe that finding the kinetic energy of the water based off of how quickly it travels the radius can potentially work, given that detonating explosions underwater are applicable used for floods and what not.
 
We rarely will see a underwater explosion causing waves in the surface in fiction, most of the time we just going to see a fireball underwater. If the explosion cause a vacuum or waves then we use KE, but there's no wave to find energy by just seing the fireball underwater.
 
Is either KE (or perhaps vaporization if was that way), or nothing else since there's no formula for underwater explosion in the same way there is for airburst or surface.
 
Use surface formula to lowball it & calc the KE of the moving water (if there's any)
 
It could work, the problem is that most of the time there's no point if reference in overpressure.
 
If there's no formula for it and the water didn't get vaporized the only way to probably do it is KE like the others said.
 
Actually, an underwater explosion shouldn't be any different than a surface explosion in formula

The only thing that'd change is that whoever is in the blast radius is going to suffer from hundreds of times more overpressure. It can reach 50,000 psi for the upper bound.
 
Kinetic energy of the water should only be used if the water is shown being blown back, because logically the water wouldn't move at all, since the energy would propagate cleanly through it.

This site helps with that. We're talking between 1,000, 10,000 and 50,000 pi.

10,000 psi is 689 bar

An explosion with 100m radius underwater would have a yield of:

  • W = 100^3*((27136*689 + 8649)^(1/2)/13568 - 93/13568)^2 = 97.286 kilotons of TNT (Town level+)
Overpressure is S-tier, but this is a high end.
 
That makes me think... To what clients is directed that device? You need at the very least 8.87 kg of tnt to use that thing. It also seems weird since 10 psi is the minimal amount of overpressure requiered to destroy reinforced structures, and 1k should be able to shatter any material, including sensors.

Unless, or course, overpressure underwater has different values for the same effects.
 
Seems we were wrong with the "there is no info" thing.

There is a paper with a formula for the peak overpressure of an underwater explosion, although it only seems applicable for real TNT explosions

A TNT with 1000lbs of charge weight generates anywhere between 880 and 7,700 PSI of overpressure
 
Using the surface formula, 1000 lb of tnt produce an overpressure of ~3141 bar at 1 m from epicenter; seems weird that the same amount of tnt yield such a wide rabge of overpressure.

Also, can you post the equation? Opening pdf in the canaima is pretty annoying for me.
 
"According to Cole's correlations (Ref. 2) for free-field underwater TNT explosions, the peak shock wave pressure (in psi) and integrated impulse per unit area (in psi•s) are given by:

  • Pm = 2.16 ├ù 10^4(W1/3)/R)1.13
  • I/A = 1.46 W<su9>0.63</sup>/R0.89
where W is the charge weight in pounds and R is the range in feet. Therefore, for a given charge weight the peak shock wave pressure would be expected to vary as (1/R)1.13.

The first formula is the one we're looking for.
 
This paper also explains the difference in ovrpressure between surface explosions and underwater ones, and contains quite a few tables with PSI values for some underwater blasts.

It should definitely be looked into in depth.
 
Interesting, are the values of reference the same used in the other 2 formulas? I mean, 20 psi for violent damage to reinforced structures plus 99% of fatalities, 10 psi the minimal for minimal pressure to destroy reinforced structures, etc.
 
Also, scratch what I said about a 1000lb TNT generating 880-7,700 psi of overpressure underwater. That was a surface explosion table.

There are a few underwater explosion tables, though. And in the last one they detonate TNT on a small pool and get ridiculous results of PSI, like 19,000 PSI for the eastern wall of the pool and 27,000 on the south wall.
 
From their conclusion:

"Cole also indicates that the initial shock wave entering the water at the surface of the charge can have a pressure of 2,000,000 psi and that a 300-lb TNT charge with a gas bubble radius of above 20 ft would have a shock overpressure of 34,000 psi within the gas bubble at R = 5 ft. Based on these pressure results (which are far beyond the mechanical strength of materials), any equipment or structures within the gas bubble formed by the explosion would be at risk for damag".

DontTalk should weigh in on this.
 
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